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Tunnel magnetoresistance (TMR) is a magnetoresistive effect that occurs in a magnetic tunnel junction (MTJ), which is a component consisting of two
ferromagnet Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...
s separated by a thin insulator. If the insulating layer is thin enough (typically a few
nanometre 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
s),
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s can
tunnel A tunnel is an underground passageway, dug through surrounding soil, earth or rock, and enclosed except for the entrance and exit, commonly at each end. A pipeline is not a tunnel, though some recent tunnels have used immersed tube cons ...
from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly
quantum mechanical Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
phenomenon. Magnetic tunnel junctions are manufactured in
thin film A thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ap ...
technology. On an industrial scale the film deposition is done by magnetron
sputter deposition Sputter deposition is a physical vapor deposition (PVD) method of thin film deposition by the phenomenon of sputtering. This involves ejecting material from a "target" that is a source onto a "substrate" such as a silicon wafer. Resputtering is re ...
; on a laboratory scale
molecular beam epitaxy Molecular-beam epitaxy (MBE) is an epitaxy method for thin-film deposition of single crystals. MBE is widely used in the manufacture of semiconductor devices, including transistors, and it is considered one of the fundamental tools for the devel ...
,
pulsed laser deposition Pulsed laser deposition (PLD) is a physical vapor deposition (PVD) technique where a high-power pulsed laser beam is focused inside a vacuum chamber to strike a target of the material that is to be deposited. This material is vaporized from the t ...
and
electron beam physical vapor deposition Electron-beam physical vapor deposition, or EBPVD, is a form of physical vapor deposition in which a target anode is bombarded with an electron beam given off by a charged tungsten filament under high vacuum. The electron beam causes atoms from the ...
are also utilized. The junctions are prepared by
photolithography In integrated circuit manufacturing, photolithography or optical lithography is a general term used for techniques that use light to produce minutely patterned thin films of suitable materials over a substrate, such as a silicon wafer, to protect ...
.


Phenomenological description

The direction of the two
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
s of the ferromagnetic films can be switched individually by an external
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. If the magnetizations are in a parallel orientation it is more likely that
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s will tunnel through the insulating film than if they are in the oppositional (antiparallel) orientation. Consequently, such a junction can be switched between two states of
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...
, one with low and one with very high resistance.


History

The effect was originally discovered in 1975 by Michel Jullière (University of Rennes, France) in Fe/ Ge- O/ Co-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention. In 1991 Terunobu Miyazaki (
Tohoku University , or is a Japanese national university located in Sendai, Miyagi in the Tōhoku Region, Japan. It is informally referred to as . Established in 1907, it was the third Imperial University in Japan and among the first three Designated National ...
, Japan) found a change of 2.7% at room temperature. Later, in 1994, Miyazaki found 18% in junctions of iron separated by an
amorphous In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wi ...
aluminum oxide insulator and
Jagadeesh Moodera Jagadeesh Subbaiah Moodera is an American physicist of Indian origin and is senior research scientist at MIT's Francis Bitter Magnet Laboratory. In 1994 together with the MIT research team led by P.M. Tedrow and R. Meservey, they showed a pract ...
found 11.8% in junctions with electrodes of CoFe and Co. The highest effects observed at this time with aluminum oxide insulators was around 70% at room temperature. Since the year 2000, tunnel barriers of
crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...
magnesium oxide Magnesium oxide ( Mg O), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions ...
(MgO) have been under development. In 2001 Butler and Mathon independently made the theoretical prediction that using
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
as the ferromagnet and
MgO Magnesium oxide ( Mg O), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions ...
as the insulator, the tunnel magnetoresistance can reach several thousand percent. The same year, Bowen et al. were the first to report experiments showing a significant TMR in a MgO based magnetic tunnel junction e/MgO/FeCo(001) In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200% TMR at room temperature. In 2008, effects of up to 604% at room temperature and more than 1100% at 4.2 K were observed in junctions of CoFeB/MgO/CoFeB by S. Ikeda, H. Ohno group of Tohoku University in Japan.


Applications

The read-heads of modern
hard disk drive A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
s work on the basis of magnetic tunnel junctions. TMR, or more specifically the magnetic tunnel junction, is also the basis of
MRAM Magnetoresistive random-access memory (MRAM) is a type of non-volatile random-access memory which stores data in magnetic domains. Developed in the mid-1980s, proponents have argued that magnetoresistive RAM will eventually surpass competing tec ...
, a new type of
non-volatile memory Non-volatile memory (NVM) or non-volatile storage is a type of computer memory that can retain stored information even after power is removed. In contrast, volatile memory needs constant power in order to retain data. Non-volatile memory typic ...
. The 1st generation technologies relied on creating cross-point magnetic fields on each bit to write the data on it, although this approach has a scaling limit at around 90–130 nm.Barry Hoberma
The Emergence of Practical MRAM
. Crocus Technologies
There are two 2nd generation techniques currently being developed: Thermal Assisted Switching (TAS) and
Spin-transfer torque Spin-transfer torque (STT) is an effect in which the orientation of a magnetic layer in a magnetic tunnel junction or spin valve can be modified using a spin-polarized current. Charge carriers (such as electrons) have a property known as spin ...
. Magnetic tunnel junctions are also used for sensing applications. Today they are commonly used for position sensors and current sensors in various automotive, industrial and consumer applications. These higher performance sensors are replacing Hall sensors in many applications due to their improved performance.


Physical explanation

The relative resistance change—or effect amplitude—is defined as :\mathrm := \frac where R_\mathrm is the electrical resistance in the anti-parallel state, whereas R_\mathrm is the resistance in the parallel state. The TMR effect was explained by Jullière with the
spin polarization Spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in fe ...
s of the ferromagnetic electrodes. The spin polarization ''P'' is calculated from the
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
dependent
density of states In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states i ...
(DOS) \mathcal at the
Fermi energy The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi ga ...
: P = \frac The spin-up electrons are those with spin orientation parallel to the external magnetic field, whereas the spin-down electrons have anti-parallel alignment with the external field. The relative resistance change is now given by the spin polarizations of the two ferromagnets, ''P1'' and ''P2'': \mathrm = \frac If no
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage ''U'', electrons tunnel preferentially to the positive electrode. With the assumption that spin is conserved during tunneling, the current can be described in a two-current model. The total current is split in two partial currents, one for the spin-up electrons and another for the spin-down electrons. These vary depending on the magnetic state of the junctions. There are two possibilities to obtain a defined anti-parallel state. First, one can use ferromagnets with different coercivities (by using different materials or different film thicknesses). And second, one of the ferromagnets can be coupled with an
antiferromagnet In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. ...
(
exchange bias Exchange bias or exchange anisotropy occurs in bilayers (or multilayers) of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film. The ex ...
). In this case the magnetization of the uncoupled electrode remains "free". The TMR becomes infinite if ''P1'' and ''P2'' equal 1, i.e. if both electrodes have 100% spin polarization. In this case the magnetic tunnel junction becomes a switch, that switches magnetically between low resistance and infinite resistance. Materials that come into consideration for this are called ''ferromagnetic half-metals''. Their conduction electrons are fully spin-polarized. This property is theoretically predicted for a number of materials (e.g. CrO2, various
Heusler alloy Heusler compounds are magnetic intermetallics with face-centered cubic crystal structure and a composition of XYZ (half-Heuslers) or X2YZ (full-Heuslers), where X and Y are transition metals and Z is in the p-block. The term derives from the name ...
s) but its experimental confirmation has been the subject of subtle debate. Nevertheless, if one considers only those electrons that enter into transport, measurements by Bowen et al. of up to 99.6% spin polarization at the interface between La0.7Sr0.3MnO3 and SrTiO3 pragmatically amount to experimental proof of this property. The TMR decreases with both increasing temperature and increasing bias voltage. Both can be understood in principle by
magnon A magnon is a quasiparticle, a collective excitation of the electrons' spin structure in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of e ...
excitations and interactions with magnons, as well as due to tunnelling with respect to localized states induced by oxygen vacancies (see Symmetry Filtering section hereafter).


Symmetry-filtering in tunnel barriers

Prior to the introduction of epitaxial
magnesium oxide Magnesium oxide ( Mg O), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions ...
(MgO), amorphous aluminum oxide was used as the tunnel barrier of the MTJ, and typical room temperature TMR was in the range of tens of percent. MgO barriers increased TMR to hundreds of percent. This large increase reflects a synergetic combination of electrode and barrier electronic structures, which in turn reflects the achievement of structurally ordered junctions. Indeed, MgO filters the tunneling transmission of electrons with a particular symmetry that are fully spin-polarized within the current flowing across
body-centered cubic In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of ...
Fe-based electrodes. Thus, in the MTJ's parallel (P) state of electrode magnetization, electrons of this symmetry dominate the junction current. In contrast, in the MTJ's antiparallel (AP) state, this channel is blocked, such that electrons with the next most favorable symmetry to transmit dominate the junction current. Since those electrons tunnel with respect to a larger barrier height, this results in the sizeable TMR. Beyond these large values of TMR across MgO-based MTJs, this impact of the barrier's electronic structure on tunnelling spintronics has been indirectly confirmed by engineering the junction's potential landscape for electrons of a given symmetry. This was first achieved by examining how the electrons of a
lanthanum strontium manganite Lanthanum strontium manganite (LSM or LSMO) is an oxide ceramic material with the general formula La1−xSrxMnO3, where ''x'' describes the doping level. It has a Perovskite (structure), perovskite-based crystal structure, which has the general f ...
half-metal A half-metal is any substance that acts as a conductor to electrons of one spin orientation, but as an insulator or semiconductor to those of the opposite orientation. Although all half-metals are ferromagnetic (or ferrimagnetic), most ferroma ...
lic electrode with both full spin (P=+1 ) and symmetry polarization tunnel across an electrically biased SrTiO3 tunnel barrier. The conceptually simpler experiment of inserting an appropriate metal spacer at the junction interface during sample growth was also later demonstrated . While theory, first formulated in 2001, predicts large TMR values associated with a 4eV barrier height in the MTJ's P state and 12eV in the MTJ's AP state, experiments reveal barrier heights as low as 0.4eV. This contradiction is lifted if one takes into account the localized states of oxygen vacancies in the MgO tunnel barrier. Extensive solid-state tunnelling spectroscopy experiments across MgO MTJs revealed in 2014 that the electronic retention on the ground and excited states of an oxygen vacancy, which is temperature-dependent, determines the tunnelling barrier height for electrons of a given symmetry, and thus crafts the effective TMR ratio and its temperature dependence. This low barrier height in turn enables the high current densities required for spin-transfer torque, discussed hereafter.


Spin-transfer torque in magnetic tunnel junctions (MTJs)

The effect of
spin-transfer torque Spin-transfer torque (STT) is an effect in which the orientation of a magnetic layer in a magnetic tunnel junction or spin valve can be modified using a spin-polarized current. Charge carriers (such as electrons) have a property known as spin ...
has been studied and applied widely in MTJs, where there is a tunnelling barrier sandwiched between a set of two ferromagnetic electrodes such that there is (free) magnetization of the right electrode, while assuming that the left electrode (with fixed magnetization) acts as spin-polarizer. This may then be pinned to some selecting transistor in a
magnetoresistive random-access memory Magnetoresistive random-access memory (MRAM) is a type of non-volatile random-access memory which stores data in magnetic domains. Developed in the mid-1980s, proponents have argued that magnetoresistive RAM will eventually surpass competing tec ...
device, or connected to a preamplifier in a
hard disk drive A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
application. The spin-transfer torque vector, driven by the linear response voltage, can be computed from the expectation value of the torque operator: \mathbf = \mathrm hat \hat_\mathrm where \hat_\mathrm is the
gauge-invariant In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...
nonequilibrium
density matrix In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using ...
for the steady-state transport, in the zero-temperature limit, in the linear-response regime, and the torque operator \hat is obtained from the time derivative of the spin operator: \hat = \frac= -\frac\left frac\boldsymbol,\hat\right Using the general form of a 1D tight-binding Hamiltonian: \hat=\hat_0 - \Delta (\boldsymbol \cdot \mathbf)/2 where total magnetization (as macrospin) is along the unit vector \mathbf and the Pauli matrices properties involving arbitrary classical vectors \mathbf,\mathbf , given by (\boldsymbol \cdot \mathbf)(\boldsymbol \cdot \mathbf) = \mathbf \cdot \mathbf + i(\mathbf\times\mathbf)\cdot \boldsymbol (\boldsymbol \cdot \mathbf) \boldsymbol = \mathbf + i \boldsymbol \times \mathbf \boldsymbol (\boldsymbol \cdot \mathbf) = \mathbf + i \mathbf \times \boldsymbol it is then possible to first obtain an analytical expression for \hat (which can be expressed in compact form using \Delta, \mathbf , and the vector of Pauli spin matrices \boldsymbol=(\sigma_x,\sigma_y,\sigma_z) ). The spin-transfer torque vector in general MTJs has two components: a parallel and perpendicular component: A parallel component: T_=\sqrt And a perpendicular component: T_=T_y In symmetric MTJs (made of electrodes with the same geometry and exchange splitting), the spin-transfer torque vector has only one active component, as the perpendicular component disappears: T_ \equiv 0 . Therefore, only T_ vs. \theta needs to be plotted at the site of the right electrode to characterise tunnelling in symmetric MTJs, making them appealing for production and characterisation at an industrial scale. Note: In these calculations the active region (for which it is necessary to calculate the retarded
Green's function In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential ...
) should consist of the tunnel barrier + the right ferromagnetic layer of finite thickness (as in realistic devices). The active region is attached to the left ferromagnetic electrode (modeled as semi-infinite tight-binding chain with non-zero
Zeeman splitting The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
) and the right N electrode (semi-infinite tight-binding chain without any Zeeman splitting), as encoded by the corresponding self-energy terms.


Discrepancy between theory and experiment

Theoretical tunnelling magneto-resistance ratios of 10000% have been predicted. However, the largest that have been observed are only 604%. One suggestion is that
grain boundaries In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional crystallographic defect, defects in the crystal structure, and tend to decrease the ...
could be affecting the insulating properties of the MgO barrier; however, the structure of films in buried stack structures is difficult to determine. The grain boundaries may act as short circuit conduction paths through the material, reducing the resistance of the device. Recently, using new
scanning transmission electron microscopy A scanning transmission electron microscope (STEM) is a type of transmission electron microscope (TEM). Pronunciation is tɛmor sti:i:ɛm As with a conventional transmission electron microscope (CTEM), images are formed by electrons passing ...
techniques, the grain boundaries within FeCoB/MgO/FeCoB MTJs have been atomically resolved. This has allowed first principles
density functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
calculations to be performed on structural units that are present in real films. Such calculations have shown that the band gap can be reduced by as much as 45%. In addition to grain boundaries, point defects such as boron interstitial and oxygen vacancies could be significantly altering the tunnelling magneto-resistance. Recent theoretical calculations have revealed that boron interstitials introduce defect states in the band gap potentially reducing the TMR further These theoretical calculations have also been backed up by experimental evidence showing the nature of boron within the MgO layer between two different systems and how the TMR is different.


See also

*
Quantum tunneling In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
*
Magnetoresistance Magnetoresistance is the tendency of a material (often ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk ...
*
Giant Magnetoresistance Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter ...
(GMR) *
Spin-transfer torque Spin-transfer torque (STT) is an effect in which the orientation of a magnetic layer in a magnetic tunnel junction or spin valve can be modified using a spin-polarized current. Charge carriers (such as electrons) have a property known as spin ...


References

{{DEFAULTSORT:Tunnel Magnetoresistance Electric and magnetic fields in matter Spintronics Magnetoresistance